Nilpotent orbits and Whittaker functions for derived functor modules of Sp(2, ℝ)

We study the moderate growth generalized Whittaker functions, associated to a unitary character ψ of a unipotent subgroup, for the non-tempered cohomological representation of G = Sp (2, ℝ). Through an explicit calculation of a holonomic system which characterizes these functions we observe that their existence is determined by the including relation between the real nilpotent coadjoint G-orbit of ψ in g*_ℝ and the asymptotic support of the cohomological representation.